VIBRATION ANALYSIS OF MECHANICAL SYSTEMS WITH MULTIPLE DEGREES OF FREEDOM USING PYTHON

Abstract

This study investigates the dynamic behavior of a discrete multi-mass structure, which is highly relevant for engineers seeking to predict and control structural oscillations. The research starts from the hypothesis that numerical modeling and simulation can effectively describe coupled oscillations in systems with several masses and elastic connections. The main objective is to build and solve the equations of motion for a simple multi-degree-of-freedom model using an open-source programming approach. The theoretical background is explained concisely, while the equations are solved numerically with a Python implementation using standard scientific libraries. Modal analysis, eigenvalue computation and time-domain simulation are performed, and the results demonstrate the distribution of energy and the effects of damping. The combined response is visualized through both classic plots and an innovative 3D representation of the coupled displacements. This work confirms that flexible, free numerical tools can be applied successfully to dynamic studies and provides a clear example for engineering education and applied research.